document.write( "Question 253818: Two roots of a polynomial equation with real coefficients are 2+3i and square root of 7. Then find two additional roots. Then find the degree of the polynomial. \n" ); document.write( "

Algebra.Com's Answer #186154 by drk(1908) $\"\"$ $\"About$

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FIrst we are given 2 roots:
\n" ); document.write( " $\"2%2B3i\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+sqrt%287%29\"$ .
\n" ); document.write( "The other 2 roots are
\n" ); document.write( " $\"2-3i\"$
\n" ); document.write( "and
\n" ); document.write( " $\"-sqrt%287%29\"$
\n" ); document.write( "These are both conjugates.
\n" ); document.write( "So, we have a polynomial expressed as
\n" ); document.write( " $\"%28x-%282%2B3i%29%29%28x-%282-3i%29%29%28x-sqrt%287%29%29%28x%2Bsqrt%287%29%29\"$
\n" ); document.write( "this can be simplified to
\n" ); document.write( " $\"%28x%5E2-4x+%2B+13%29%28x%5E2-7%29\"$
\n" ); document.write( "and then to
\n" ); document.write( " $\"x%5E4-4x%5E3%2B6x-91\"$ \n" ); document.write( "

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